In this article, a wideband circularly polarized (CP) transmitarray antenna (TA) operating at the X-band is reported. A receive-and-transmit type anisotropic magneto-electric (ME) dipole is proposed as the broadband TA unit cell with low-insertion-loss characteristic. By employing the element rotation methodology, the continuous transmissive phase compensation is achieved, thus producing the high-gain directive radiation. The 16×16-element CP TA implemented using the designed ME-dipole structure not only possesses wide measured 1-dB and 3-dB gain bandwidths of 24.5% (10.75-13.75 GHz) and 33.3% (10-14 GHz), respectively, but also yields a notable 1.5-dB axial ratio (AR) bandwidth of 37.4% (9.25-13.5 GHz). Peak gain of 24.3 dBic and aperture efficiency of 46% are experimentally measured. The proposed CP TA shows attractive advantages including wide bandwidth, high-purity circular polarization and stable gain, which makes it a competitive candidate for many applications including satellite communication (SatCom).